Chứng minh :22015<5863
Chứng minh rằng: 12015 + 22015 + ..... + 20152015 chia hết cho 1 + 2 + ... + 2015.
2x+1.22014 = 22015.
c) 2 2016 . 2 x - 1 = 2 2015
c) 2 2016 . 2 x - 1 = 2 2015
2 x - 1 = 2 2015 : 2 2016
2 x - 1 = 2 2015 - 2016
2 x - 1 = 2 - 1
⇒ x – 1 = -1
x = -1 + 1
x = 0
A = 1 + 21 + 22 + ... + 22015
\(A=1+2^1+2^2+...+2^{2015}\)
\(2\cdot A=2^1+2^2+2^3+...+2^{2015}+2^{2016}\)
\(2A-A=2^1+2^2+2^3+...+2^{2015}+2^{2016}-\left(1+2^1+2^2+...+2^{2015}\right)\)
\(A=2^{2016}-1\)
4 + 22 + 23 + 24 + … + 22015 = 2x
tìm x:
2x + 1 . 22014= 22015
\(2^{x+1}\cdot2^{2014}=2^{2015}\\ 2^{x+1}=2^{2015}:2^{2014}\\ 2^{x+1}=2\\ =>x+1=1\\ x=1-1\\ x=0\)
B = 22018 - 22017 - 22016 - 22015 - 22014
\(B=2^{2018}-2^{2017}-2^{2016}-2^{2015}-2^{2014}\)
\(=>2B=2^{2019}-2^{2018}-2^{2017}-2^{2016}-2^{2015}\)
\(=>2B+B=2^{2019}-2^{2014}\)
\(=>B=\dfrac{2^{2019}-2^{2014}}{3}\)
A=22015*72020 nhan 1 bieu thuc
Tính tổng: A = 1+21 + 22 + 23 + 24 + .... + 22015
`#3107`
\(A=1+2^1+2^2+2^3+...+2^{2015}\)
\(2A=2+2^2+2^3+2^4+...+2^{2016}\)
\(2A-A=\left(2+2^2+2^3+2^4+...+2^{2016}\right)-\left(1+2+2^2+2^3+...+2^{2015}\right)\)
\(A=2+2^2+2^3+2^4+...+2^{2016}-1-2-2^2-2^3-...-2^{2015}\)
\(A=2^{2016}-1\)
Vậy, \(A=2^{2016}-1.\)
\(A=2^0+2^1+2^2+...+2^{2015}\)
\(2\cdot A=2^1+2^2+2^3+...+2^{2016}\)
\(A=2A-A=2^{2016}-2^0\)
\(A=2^{2016}-1\)
Tính phần nguyên của thương: 24587556758493847584938475241586958 và 22015